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Accounting for the speed shear in wind turbine power performance measurement

Wagner, Rozenn

Publication date:2010

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Citation (APA):Wagner, R. (2010). Accounting for the speed shear in wind turbine power performance measurement. RisøNational Laboratory for Sustainable Energy. Risø-PhD No. 58(EN)

https://orbit.dtu.dk/en/publications/1ba83f85-6178-45ab-8997-440a646f4577

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Accounting for the speed shear in wind turbine power performance measurement

Rozenn Wagner Risø-PhD-58(EN) - Short version April 2010

Author: Rozenn WagnerTitle: Accounting for the speed shear in wind turbine powerperformance measurementDivision: Wind Energy Division

Abstract:

The power curve of a wind turbine is the primary char-acteristic of the machine as it is the basis of the warranty forit power production. The current IEC standard for powerperformance measurement only requires the measurementof the wind speed at hub height and the air density tocharacterise the wind field in front of the turbine. However,with the growing size of the turbine rotors during the lastyears, the effect of the variations of the wind speed within theswept rotor area, and therefore of the power output, cannot beignored any longer. Primary effects on the power performanceare from the vertical wind shear and the turbulence intensity.The work presented in this thesis consists of the descriptionand the investigation of a simple method to account for thewind speed shear in the power performance measurement. Ig-noring this effect was shown to result in a power curve depen-dant on the shear condition, therefore on the season and thesite. It was then proposed to use an equivalent wind speedaccounting for the whole speed profile in front of the turbine.The method was first tested with aerodynamic simulations of amulti-megawatt wind turbine which demonstrated the decreaseof the scatter in the power curve. A power curve defined interms of this equivalent wind speed would be less dependanton the shear than the standard power curve.The equivalent wind speed method was then experimentallyvalidated with lidar measurements. Two equivalent wind speeddefinitions were considered both resulting in the reduction ofthe scatter in the power curve. As a lidar wind profiler canmeasure the wind speed at several heights within the rotorspan, the wind speed profile is described with more accuracythan with the power law model. The equivalent wind speedderived from measurements, including at least one measure-ment above hub height, resulted in a smaller scatter in thepower curve than the equivalent wind speed derived from pro-files extrapolated from measurements at hub height and belowonly.It is well established that the turbulence intensity also influ-ences the power performance of a wind turbine. Two ways ofaccounting for the turbulence were tested with the experimen-tal data: an adaptation of the equivalent wind speed so that italso accounts for the turbulence intensity and the combinationof the equivalent wind speed accounting for the wind shearonly with the turbulence normalising method for turbulenceintensity suggested by Albers. The second method was foundto be more suitable for normalising the power curve for theturbulence intensity.Using the equivalent wind speed accounting for the wind shearin the power performance measurement was shown to result ina more repeatable power curve than the standard power curveand hence, in a better annual energy production estimation.Furthermore, the decrease of the scatter in the power curvecorresponds to a decrease of the category A uncertainty inpower, resulting in a smaller uncertainty in estimated AEP.

The thesis is submitted to the Danish Technical Univer-sity in partial fulfilment of the requirements for the PhDdegree.

Risø-PhD-58(EN)April 2010

ISBN 978-87-550-3816-5

Contract no.:

Group’s own reg. no.:

Sponsorship:ModObs Network MRTN-CT-2006-019369

Pages:155References:53

Information Service DepartmentRisøNational Laboratory forSustainable EnergyTechnical University of DenmarkP.O.Box 49DK-4000 RoskildeDenmarkTelephone +45 [email protected] +45 46774013www.risoe.dtu.dk

Contents

Acknowledgements 9

1 Introduction 11

2 Wind profiles 152.1 Effects governing the wind speed profile . . . . . . . . . . . . . . . . . . . 15

2.1.1 Geostrophic wind and friction of the surface . . . . . . . . . . . . . 152.1.2 Static stability of the ABL . . . . . . . . . . . . . . . . . . . . . . 152.1.3 Local effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Wind speed profiles at Høvsøre . . . . . . . . . . . . . . . . . . . . . . . . 172.2.1 Høvsøre test site . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.2 Wind shear at Høvsøre . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Wind speed profile characterisation . . . . . . . . . . . . . . . . . . . . . . 182.3.1 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3.2 The logarithmic wind profile . . . . . . . . . . . . . . . . . . . . . 202.3.3 Vertical wind gradient . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.4 The power law profile . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.5 Comparison of methods . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Effect of speed shear 273.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Aerodynamic simulations set up . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Aerodynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Model limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Effect of the wind speed shear on the aerodynamics of the turbine . . . . 313.3.1 Free wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3.2 Relative speed and angle of attack . . . . . . . . . . . . . . . . . . 323.3.3 Tangential force and Torque . . . . . . . . . . . . . . . . . . . . . . 33

3.4 Consequences on the power production . . . . . . . . . . . . . . . . . . . . 333.5 Consequences on the power curve . . . . . . . . . . . . . . . . . . . . . . . 35

3.5.1 With power law profiles . . . . . . . . . . . . . . . . . . . . . . . . 353.5.2 With other wind speed profiles . . . . . . . . . . . . . . . . . . . . 36

3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 Effect of turbulence intensity 374.1 Isolated turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.1 Simple aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1.2 Consequences on the power curve . . . . . . . . . . . . . . . . . . . 38

4.2 Turbulence and shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2.1 With power law profiles . . . . . . . . . . . . . . . . . . . . . . . . 404.2.2 With other wind speed profiles . . . . . . . . . . . . . . . . . . . . 41

4.3 Summary of the turbulence effect . . . . . . . . . . . . . . . . . . . . . . . 41

Risø–PhD–58(EN)

6 CONTENTS

5 Equivalent wind speed 435.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2 Equivalent wind speed for shear . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2.1 With power law profiles . . . . . . . . . . . . . . . . . . . . . . . . 445.2.2 With other wind speed profiles . . . . . . . . . . . . . . . . . . . . 46

5.3 Equivalent wind speed and turbulence . . . . . . . . . . . . . . . . . . . . 475.3.1 Reduction of the scatter with turbulent inflow . . . . . . . . . . . . 475.3.2 Scatter due to turbulence . . . . . . . . . . . . . . . . . . . . . . . 47

5.4 Summary of equivalent wind speed investigation with aerodynamic simu-lations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6 Lidar 516.1 Principle of operation of a pulsed lidar . . . . . . . . . . . . . . . . . . . . 51

6.1.1 Measurement range . . . . . . . . . . . . . . . . . . . . . . . . . . 526.1.2 Radial speed retrieval . . . . . . . . . . . . . . . . . . . . . . . . . 536.1.3 Three-dimensional vector . . . . . . . . . . . . . . . . . . . . . . . 536.1.4 Carrier to Noise Ratio . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.2 Limitations of a pulsed lidar in measuring the wind speed profile . . . . . 556.2.1 Horizontal homogeneity . . . . . . . . . . . . . . . . . . . . . . . . 556.2.2 Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.2.3 Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.3 Other remote sensing wind profilers . . . . . . . . . . . . . . . . . . . . . . 566.3.1 Continuous wave lidar . . . . . . . . . . . . . . . . . . . . . . . . . 566.3.2 Sodar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

7 First experiment 597.1 Description of the measurement campaign . . . . . . . . . . . . . . . . . . 597.2 Comparison Lidar-Sodar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607.3 Power curve measurement with the lidar . . . . . . . . . . . . . . . . . . . 61

7.3.1 Direct comparison to the standard power curve . . . . . . . . . . . 617.3.2 Lidar correction with the cup anemometer measurements . . . . . 627.3.3 Spatial correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . 647.3.4 Shear distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7.4 Conclusions of the first measurement campaign . . . . . . . . . . . . . . . 66

8 Second experiment 698.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698.2 Description of the experiment . . . . . . . . . . . . . . . . . . . . . . . . . 698.3 Using the lidar to measure a standard power curve . . . . . . . . . . . . . 708.4 Wind shear effect on the power performance measurement . . . . . . . . . 728.5 A better approximation of the kinetic energy flux . . . . . . . . . . . . . . 748.6 Application of the equivalent wind speed method . . . . . . . . . . . . . . 75

8.6.1 Application to the classified profiles . . . . . . . . . . . . . . . . . 758.6.2 Application to the unified data set . . . . . . . . . . . . . . . . . . 75

8.7 Lidar profiles corrected with cup anemometer measurements . . . . . . . . 768.8 Conclusions of the second experiment . . . . . . . . . . . . . . . . . . . . 77

9 Further investigations of the equivalent wind speed using real data 819.1 Various definitions of equivalent wind speed . . . . . . . . . . . . . . . . . 819.2 Speed profile description for the application of the equivalent speed method 83

9.2.1 Number of measurement points in the speed profile . . . . . . . . . 849.2.2 With extrapolated profiles . . . . . . . . . . . . . . . . . . . . . . . 869.2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

9.3 Combination of the equivalent wind speed method with Albers’ method . 879.3.1 Description of Albers’ method . . . . . . . . . . . . . . . . . . . . 879.3.2 Combination with the equivalent wind speed . . . . . . . . . . . . 89


CONTENTS 7

10 Annual Energy Production 9310.1 Direct comparison of the standard and equivalent wind speed power curves 9310.2 AEP prediction and transferable power curve . . . . . . . . . . . . . . . . 9510.3 How should the equivalent wind speed be used to estimate the AEP? . . . 96

11 Measurement uncertainty 9911.1 Power curve uncertainty in the IEC 61400-12-1 standard . . . . . . . . . . 9911.2 Lidar calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

11.2.1 Calibration coefficient at verification heights . . . . . . . . . . . . . 10011.2.2 Calibration coefficient at any height . . . . . . . . . . . . . . . . . 100

11.3 Definition of the uncertainty in measurements for a calibrated lidar . . . . 10311.3.1 Uncertainty at verification heights . . . . . . . . . . . . . . . . . . 10311.3.2 Uncertainty at any height . . . . . . . . . . . . . . . . . . . . . . . 103

11.4 Uncertainty in equivalent wind speed . . . . . . . . . . . . . . . . . . . . . 10311.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

11.5.1 Power curve uncertainty . . . . . . . . . . . . . . . . . . . . . . . . 10511.5.2 AEP uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

11.6 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

12 Discussion and further work 10912.1 Equivalent wind speed method . . . . . . . . . . . . . . . . . . . . . . . . 10912.2 Lidar measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

13 Conclusions 113

Bibliography 115

Appendix 119

Paper I 121

Paper II 123


Acknowledgements

First of all, I would like to thank a lot my supervisor, Mike Courtney, for his great supportand assistance, and the time devoted to constructive ”hair-pulling”. He was always readyto help me and it was a pleasure to be his student. I also thank all my colleagues fromthe Test and Measurement group, in particular Uwe Paulsen, Troels Friis Pedersen, AllanVesth, Petter Lindelöw-Marsden and Julia Gottshall for the very interesting discussionsand showing so much interest in my work, which helped to carry on towards resultsrelevant for the wind energy community. Moreover, Per Hansen, Bjarne Sønderskov andAnders R. Vestergaard were very helpful with all the technical and experimental work.

Torben J. Larsen and Helge A. Madsen, from the AED group, are thanked for theirvery valuable help and support with the aerodynamic simluations.

I am very grateful to my first supervisors, Ioannis Antoniou and Hans Jørgensen, forgetting me started at Risø, assisting me at the beginning of the PhD and keeping an eyeon my progress during the 3 years.

Many thanks to my friends and various office mates: especially to Alfredo and Ferhatfor their scientific inputs and valuable advice, and to the ”girl office”, Claire, Carolineand Ioanna, for their support and the good atmosphere. A special thank to Eleni for herfriendship and for always being game for activities that cut off from work.

Merci à Julien, pour m’avoir accompagnée au Danemark et pour son soutien moralet materiel, en particulier durant la rédaction. Merci à mes parents pour leurs constantsencouragements et pour avoir toujours cru en moi.

I acknowledge the PhD funding from the ModObs Network MRTN-CT-2006-019369and from Vestas Wind Systems A/S. Many thanks to Anna-Maria Sempreviva for initi-ating and organising the ModObs network.

I thank Siemens Wind Power and Vestas Wind System A/S for permission to use theturbine data. I acknowledge the support from IMPER project financed by the DanishEnergy Agency (journal no.: 3302-0106), the EU Upwind project (WP6) and the EUSafeWind project (WP2) in the experimental part of the work.


Chapter 1

Introduction

Power curves are central to the wind industry as they form the basis for the powerproduction warranty of the turbine. Indeed, power curves are frequently presented byturbine manufacturers in their marketing literature. They are of utmost relevance to thewind farm developers in order to chose the turbine best suited to the wind resources ofthe site and, in conjunction with the wind resource, to predict the energy production ofthe farm. Once the turbine is installed, the power curve is again of importance since it isnecessary to check that the energy production meets that promised by the manufacturer.

The power curve of a wind turbine is a representation of its performance. It showsthe power output of the turbine as a function of the wind speed input. Figure 1.1 showsa typical wind turbine power curve. The cut-in wind speed (ucut−in) is the minimumwind speed at which the wind turbine starts to produce power. For wind speeds abovethe cut-in speed, the power increases with the wind speed until reaching the rated power(Prated), i.e. the maximum power the turbine can produce. The wind speed for which therated power is first reached is named the rated wind speed (urated). Between rated windspeed and cut-out wind speed (namely the wind speed for which the wind turbine shutsdown, ucut−out), the control system of the turbine maintains the power output constantat rated power, by pitching the blades.

ucut�in urated ucut�outWind speed �m�s�

Prated

Electrical power �kW�

Figure 1.1: Typical wind turbine power curve

It is common practice to validate predictions of wind turbine power curves madewith computational models by using measured data. Over the past decade, considerableadvances have been made in achieving consistency in the measurement of wind turbinepower curves. Since the publication in 1998, the IEC 61400-12 (IEC, 1998a) standardis now widely accepted as the contractual guidance for power curve measurement. Thisstandard was withdrawn in 2005 and replaced by the IEC standard 61400-12-1 (IEC,2005). According to this standard, the power performance of a wind turbine is achievedby measuring the wind speed with a cup anemometer mounted on top of a mast with thesame height as the hub of the turbine and located at a distance of 2 to 4 rotor diameters


12 Introduction

in front of the turbine (2.5 rotor diameters is recommended). As the air density causesvariation in the wind kinetic energy flux through the rotor swept area, the wind speed1

is normalised to the sea level air density. Simultaneous 10 minute mean wind speed and10 minute mean power give the power curve scatter plot. These points are averaged inwind speed bins of 0.5 m/s resulting in the mean measured power curve.

The scatter in the power curve scatter plot is due to various factors which affect thewind turbine performance. These factors can be grouped in 3 categories:

1. the turbine operation including the blades conditions and the control algorithm forexample;

2. the measurement errors due to the instruments such as the anemometer and thepower sensor;

3. the wind conditions including the wind shear, the wind veer and the turbulence.

In this work, the effects on the scatter plot due to the wind conditions were only discussedand investigated.

The IEC 61400-12-1 standard only requires measurements of the wind speed at hubheight and the air density (derived from temperature and pressure measurements) tocharacterise the wind field surrounding the wind turbine. However it has been shown thatother wind characteristics such as the variation of the wind speed with altitude, i.e. thevertical wind shear, and the fast variation of wind speed around the 10 minute mean windspeed, which is usually referred to as turbulence, can also influence the power performanceof a large turbine. If the power performance testing of a wind turbine was sufficientlylong, then a range of conditions typical of the long term would be experienced andthere would be no particular bias introduced by ignoring such dependencies. However,performance evaluation uses quite short test durations, too short for an annual range ofweather conditions to be experienced. For this reason, power performance tests on oneturbine made at different times of the year, or for different wind direction sectors, or testsof two identical turbines located at two different sites can result in different power curves.Such power curves are hardly comparable and repeatable. There is no basis for makingconfident predictions of turbine performance at commercial sites based on limited typetesting that ignores important secondary parameters.

The effect of the wind shear and turbulence on the turbine performance is only brieflymentioned in the IEC 61400-12-1 standard. However they are recognised to possibly in-crease the uncertainty in power performance measurement. Despite this qualification, noclear recommendation about the manner of accounting for the wind shear and turbulenceeffects is given in the standard. Other authors have shown that the vertical wind shearhas an effect on the power performance. The assumption that the speed profile is con-stant over the turbine rotor (as is implicit in the IEC standard) leads to inconsistencies.The IEC 64100-12-1 standard is currently under revision and the way of accounting forthe wind shear and turbulence are amongst the main points of revision. Within thiscontext, the work presented in this thesis is focused on the effect of the vertical windshear on the power performance measurement. As the wind shear effect cannot easily beisolated from that of turbulence, turbulence effects were also investigated.

A major obstacle to the investigation of the effect of shear on the power performanceof a turbine is the lack of information available to characterise the wind profile overthe whole turbine rotor. In particular, there is seldom data available to measure thevariation of wind speed above the hub height of the machine. As the size of windturbines has considerably increased during the last few years, implying higher hubs andlarger rotors, such measurements would require very tall, and therefore costly, masts.However, at the same time, remote sensing measurement technology has significantlyimproved, in particular that of LiDAR (Light Detection And Ranging). Based on fiber

1In this work, the wind speed was normalised for air density since modern pitch regulated windturbines were considered. However, the power should be normalised for stall regulated turbines (IEC,2005).


Introduction 13

optic components available to the communication industry, lidars entered the wind energyfield about 5 years ago. Such an instrument is a quite revolutionary tool for powerperformance measurement as it enables us to obtain speed profile measurements up tothe higher tip of a multi-megawatt (multi-MW) wind turbine, relatively easily and witha good accuracy.

The work presented is this thesis had two main aims:

1. to suggest a method that can improve the power performance measurement con-cerning wind shear influence: that is the use of a wind speed equivalent to the windspeed profile in front of the turbine rotor;

2. to show the possibility of using lidar measurements for power performance mea-surement and in particular for the application of the method suggested above.

The structure of the thesis is as follows: Chapter 2 first gives a short review of themain meteorological phenomena that generate various speed profiles. Secondly, the mostcommon ways of characterising the wind shear are presented based on the analysis oflong term measurement at the Risø DTU Test Station for Large Wind Turbines wherethe experimental work was carried out.

Chapter 3 presents the investigation of the effect of shear on the power performanceof a wind turbine with aerodynamic simulations. The differences that a sheared inflowmakes on the turbine aerodynamic compared to a constant profile were shown with simplesimulation cases. The impact of a sheared inflow on the power performance was thenshown for various types of wind profile.

In order to focus on the effect of wind shear, only simulations with laminar inflowswere considered in chapter 3. However, the effect of turbulence should also be takeninto account. Thus, chapter 4 presents the investigation of the effect of turbulence onthe power curve. This investigation was also performed with aerodynamic simulations,but with turbulent inflow. Both cases of turbulence without and with wind shear werediscussed.

It is then possible to introduce the method suggested to account for the wind shear inthe power performance measurement: the use of an equivalent wind speed representativeof the wind speed profile in front of the turbine rotor. Thus, in chapter 5, the equivalentwind speed was tested with the results from the simulations described in chapter 3. Theequivalent wind speed definitions were discussed. The method was also tested withturbulent inflows (based on the simulations results presented in chapter 4).

The next step was to demonstrate the possibility of applying the equivalent windspeed method with measurements. As this required the measurement of the wind speedprofile within the range of heights swept by the turbine rotor, the lidar appeared as agood alternative to a high mast. However, lidar measurements are inherently differentfrom cup anemometer measurements in their way of operation. Chapter 6 describesthe principle of operation of a pulsed lidar system and its imitations. For comparison,the principle of operation of a continuous wave lidar and a SoDAR (Sound DetectionAnd Ranging) are briefly described with an emphasis on their differences with the pulsedlidar.

Chapter 7 describes the first measurement campaign set up with a lidar and a sodarto measure the wind profiles. Sodars have been used for wind energy assessment longerthan lidars and can also appear as a good alternative to a mast. This experiment showedthe importance of using an accurate remote sensing instrument as the wind sensor forthe power curve measurement. It was found that this requirement was met by the lidarbut not by the sodar. Furthermore, the equivalent wind speed method could not bevalidated by this experiment, because the experimental conditions were not optimal forthis purpose.

Based on what was learned from this experiment, a second measurement campaignwas undertaken. This experiment, described in chapter 8, clearly showed the effectof ignoring the speed shear in power performance measurement and the improvementobtained with the equivalent wind speed method. Firstly three definitions of equivalent


14 Introduction

wind speed accounting for the wind shear were tested and compared with the experimen-tal results. Secondly, one equivalent wind speed definition was applied with wind speedprofiles derived from different number of speed measurements (at 2, 3, 5 or 9 heights)and with profiles extrapolated from measurements below hub height. The last point ofthis chapter is the combination of the equivalent wind speed method, that “normalises”the power curve for the wind shear effect, with a method normalising the power curvefor the turbulence intensity effect.

By defining an equivalent wind speed accounting for the wind shear, a “new” powercurve different from the standard power curve was defined. Chapter 10 addressesthe problem of comparing such quantities and the consequences for the Annual EnergyProduction (AEP).

Finally, Chapter 11 presents a suggestion for evaluating the uncertainty in the powercurve obtained with the equivalent wind speed. This required the definition of the lidarmeasurement uncertainty. Thus, three kinds of power curve uncertainties were compared:the uncertainty in the power curve measurement obtained with cup anemometer mea-surements, with lidar measurements at hub height and with the equivalent wind speed(derived from lidar speed profile measurements).

Chapter 12 presents a general discussion about the equivalent wind speed concept,the use of lidar measurements in the power performance context and the limitations ofthe investigation presented. Finally, chapter 13 sums up the main conclusions that canbe drawn from this work.

During the course of the work, the influence of wind shear on the turbine powerperformance was first investigated with aerodynamic simulations. The results enabled usto define the equivalent wind speed method. Part of this investigation was published ina journal paper which is given in appendix and is referred to as Paper I in chapters 3, 4,and 5. Subsequently, the measurement campaigns where a lidar was used to measure thewind profile in front of a multi-MW wind turbine were performed in order to validate themethod. The first results of the second experiment campaign were described in a journalpaper that has been submitted for publication. Although the paper is given appendix asPaper II, the results are also presented in chapter 8 in order to maintain the consistencyof the thesis.


Chapter 2

Wind profiles

The vertical wind shear and wind veer are the variations of the wind speed and directionwith altitude, respectively. This study was focused on the vertical variation of the hori-zontal wind speed; this is what the term “wind shear” or “shear” refers to in the rest ofthe thesis if no further definition is given. This chapter starts with a short overview ofthe mechanisms generating the variation of wind speed with altitude in the atmosphericboundary layer (ABL). Then, the test site, where both experiments described in thisthesis took place, is briefly described. The wind shear characterisation is then discussedbased on observations at this site.

2.1 Effects governing the wind speed profile

The principal effects governing the properties of the boundary-layer wind are the strengthof the geostrophic wind, the surface roughness, Coriolis effects due to the Earth’s rotation,and thermal effects, i.e. the atmospheric boundary layer stability. On top of this, thewind speed profile can be influenced by local effects.

2.1.1 Geostrophic wind and friction of the surface

The geostrophic wind is the wind arising from pressure differences in the atmosphere.The pressure gradient towards a low-pressure zone causes a mass of air to accelerate alonga curve until a state of equilibrium between the pressure gradient and the Coriolis forceis reached. Therefore, in areas that are far from high-pressure or low-pressure zones, thegeostrophic wind is parallel to the isobars.

On the other hand, friction at the Earth’s surface exerts a horizontal force upon themoving air, the effect of which is to retard the flow. The surface roughness is characterizedby the density, size, and height of the buildings, trees, vegetation, rocks, etc., on theground, around and over which the wind must flow; it will be a minimum over ice oropen sea without waves and a maximum over urban areas (Dyrbye and Hansen, 1996). Aconsequence of the equilibrium of forces in the boundary layer is that the wind directioncrosses the isobars. The wind direction continues to change down through the boundarylayer and the wind speed gradually decreases to zero at the surface.

2.1.2 Static stability of the ABL

Once atmospheric pressure gradients have established the initial wind conditions, addi-tional forcing mechanisms can come into play. Since winds in the turbine layer are ofconcern here, only the mechanisms that influence the winds in the lowest levels of theatmosphere are addressed. In the surface boundary layer, over flat terrain, the windprofile is primarily influenced by the temperature gradient.

Thermal effects can be classified into three categories (Stull, 1988): stable, unstableand neutral stratification. Conditions are unstable if the potential temperature decreases


16 Wind profiles

significantly up through the atmosphere. As the warm air rises, it expands due to reducedpressure and therefore cools adiabatically. If the cooling is not sufficient to bring the airinto thermal equilibrium with the surrounding air, it continues to rise, giving advanceto large convection cells. This occurs for instance when the ground is heated by solarradiation, causing warm air near the surface to rise. The result is a thick boundarylayer with large-scale turbulent eddies. There is a lot of vertical mixing, resulting in arelatively small change of wind speed with height.

The ABL is stably stratified when the surface is cooler than the air above. If a massof air moves up in such an atmosphere, the adiabatic cooling effect causes the rising air tobecome colder than its surroundings and the mass of air moves back to its starting point.It often occurs at night when the ground surface is cold. In this situation, turbulence islimited to that due to the friction with the ground (the mixing thus remaining close tothe ground), the wind shear can be large and the flow near laminar.

In the neutral atmosphere, adiabatic cooling of the air as it rises is such that itremains in thermal equilibrium with its surroundings. This is often the case in strongwinds, when mechanical turbulence caused by ground roughness causes sufficient mixingof the boundary layer, resulting in a moderate variation in the speed profile.

For power curve purposes, the relevant wind speed range is between cut-in and ratedspeed as for higher speeds the power remains constant (see chapter 1). Therefore theABL stability has a significant influence (Sumner and Masson, 2006). Static stability ofthe lower layer of the ABL varies with season and time of day since it is primarily drivenby the magnitude and duration of the solar radiation.

Moreover, as shown by Motta et al. (2005), the diurnal and seasonal variation of thestatic stability depends on the upwind surface, e.g. offshore or onshore wind. Indeed,the heat capacity of the sea being much larger than that of land, the sea temperaturevaries much more slowly than the temperature of the land. Consequently, the diurnalvariations are much smaller over sea than over land. Moreover, this implies a shift in theseasonal variation of the stability over sea compared to the variation over a nearby landarea.

2.1.3 Local effects

Internal boundary layer

The measurement campaigns presented in this thesis were performed at a test site locatedat the west coast of Denmark (see section 2.2). The parameters influencing the wind speedprofiles at sites with upstream roughness changes are therefore of particular interest.

Roughness changes, like those at coastal sites, influence the wind speed profile. Asthe wind blows onshore from the smooth water surface to the rough land surface, theincreased friction decreases the wind speed at the lowest levels. The increased friction andthe thermal convection over land increase the turbulence generating an internal boundarylayer (IBL), see Figure 2.1. The wind speed profile above the IBL can be considered asthe same as the speed profile over the sea, but within the boundary layer, the wind speedprofile is much more complex. Indeed, as the surface roughness increases, the lower partof the profiles tends to slow down as it travels further inland. Moreover, Bergströmet al. (1988) showed that the decrease in wind speed was larger when the surface layerover land was stably stratified than when the surface layer was unstable. In the unstablesurface layer case, the wind speed decrease is smaller because the atmospheric turbulenceincreases due to enhanced buoyancy production thus compensating for the increasedfrictional losses.

The wind speed profile at a coastal site is thus influenced by the height of the IBLand it can be relevant to estimate this as a function of the distance from the coast. Inthe measurements presented by Bergström et al. (1988), the IBL height was determinedbased on the wind speed profiles at 1500 m inland and it was shown to increase from40 m for stable stratification to about 80 m during unstable stratification. A wind turbinelocated at such a site could experience profiles that deviate significantly from the classicforms such as the logarithmic or power law profiles.


Wind profiles 17

height

distance fromthe shore

IBLWind

Upwind surfaceroughness z0�u

Downwind surfaceroughness z0�d

Figure 2.1: Conceptual model of an internal boundary layer

Low level jet

A number of mechanisms produce low-level maxima in the wind speed profile. These aregenerally referred to as low level jets (LLJ). One of the main mechanisms over flat terrainis the decoupling of the flow in very stable conditions. The flow gets decoupled from thesurface friction, i.e. the wind is not affected by the surface anymore. The decouplingproduces acceleration of the flow above the atmospheric surface layer which is enhancedby the subsequent developed inertial oscillation (Stull, 1988).

LLJs are a regular feature of the night time stable boundary layer and occur veryoften in plains. This is mentioned here because references to experiments in such sitesare made later in the thesis. Banta et al. (2002) studied the characteristics of LLJs overKansas. Most of the jet maxima they measured occurred below 140m which is within theheight range swept by the rotor of a modern multi-MW wind turbine. Moreover, thesejets occurred for moderate speed (jet maxima between 7 and 10 m/s), which correspondsto the speed range where a power curve is the most sensitive to shear.

2.2 Wind speed profiles at Høvsøre

2.2.1 Høvsøre test site

Both experiments described in this thesis were performed at Risø DTU’s Test Stationfor Large Wind Turbines. This test station is located at Høvsøre, on the west coast ofDenmark. The terrain is flat, surrounded by farmland and is 1.7 km from the coast withthe North Sea. This facility comprises a line of 5 multi-MW wind turbines along theNorth-South direction parallel to the coast, see Figure 2.2. The main wind direction isfrom West and on the western side of each turbine, at a distance of 250 m (about 2.5 rotordiameters), stands a meteorological mast with a top mounted cup anemometer at theturbine’s hub height. These masts are designed and instrumented for power performancemeasurements in accordance with the IEC 61400-12-1 standard (more information aboutthe test facility in (Jørgensen et al., 2008; Courtney et al., 2008)).

At the southern end of the turbine row stands a meteorological mast (met. mast)intensively instrumented including cup anemometers at several heights between 2 m and116.5 m. These instruments were used to study the wind speed profiles. A full descriptionof the mast instrumentation is given in the appendix.

2.2.2 Wind shear at Høvsøre

In the absence of orography variations and other local effects, the wind profile is directlyaffected by the surface layer stability (Businger et al., 1971; VandenBerg, 2008; Swalwellet al., 2008). Figure 2.3 shows the average wind speed difference between 100 and 60 mat the Høvsøre met. mast by hour of the day for each season and for westerly winds (winddirection between 240◦ and 300◦) and easterly winds (wind direction between 60◦ and120◦). Since both cup anemometers are mounted on south pointing booms with similargeometry, it is assumed that the influence of the mast on both cup anemometers is equal.


18 Wind profiles

6’ 7’ 8’ 8oE 9.00’

10’ 11’ 12’

25.50’

26.00’

56oN 26.50’

27.00’

27.50’

28.00’

Turbine 5

Meteorological mast

Turbine 4

FjordNissum

Turbine 3

Turbine 2

Turbine 1

NorthSea

Figure 2.2: Sketch of the Test Station for Large Wind Turbines, Høvsøre, Denmark.

The results from the eastern sector exhibit typical variations of wind gradient influ-enced by the ABL stability, as the wind comes from the land. Clear diurnal variationscan be seen in spring and summer, whereas it is more even in winter. The diurnal varia-tions are very much attenuated in winter as the days are shorter, the heating weaker andthe temperature differences between day and night are smaller as well as those betweenair and ground.

For the western sector, where the wind comes from the sea, each histogram in Figure2.3 is rather even because there is no variation of the wind speed difference with timeof the day. The sea temperature changes too slowly to follow the diurnal pattern of thesolar radiation because of the large heat capacity of the sea. However, some differencescan be seen between the different seasons. The largest speed differences are observed inwinter and the smallest in summer. In winter, the wind speeds and the sea roughnessare higher and the prevailing conditions are stable, resulting in a larger wind shear thanin summer, where there are more unstable conditions.

An example of wind speed time series measured at different levels at the Høvsøremet. mast when the wind was from the East is shown in Figure 2.4. The surface layerstratification, characteristic of stable conditions, appears clearly during the night. Thisresults in a large wind speed shear during the night, whereas the wind speed profile isnearly flat during the day as a consequence of the convective mixing.

An example of wind speed variation for westerly winds is shown in Figure 2.5. Theshear remains rather constant all day long.

As the prevailing wind direction at Høvsøre is from the West, the wind speed pro-files considered for power curve measurements are influenced by the IBL (see section2.1.3). Moreover Enevoldsen et al. (2006) showed that peculiarities in the wind fromwest were observed at Høvsøre, especially in spring, and that the measured power curvewas significantly affected by these peculiarities. Furthermore, Nissen (2008) showed thata systematic over-speeding, compared to the traditional logarithmic wind profile, wasobserved at the top of the surface layer in spring. In order to measure a large range ofwind shears in a rather limited period of time, the measurements presented in this thesiswere taken in spring (see measurement campaigns described in chapters 7 and 8).

2.3 Wind speed profile characterisation

A categorisation of the wind shear is necessary to investigate its effect on the wind tur-bine power performance. Various methods of categorisation are generally used for windresource assessment. This section presents a review of these methods with a discussionof their use in the power performance measurement context.


Wind profiles 19

West East

Spring

0 6 12 18hour

0.5

1.0

1.5

2.0�u �m�s�

0 6 12 18hour

0.5

1.0

1.5

2.0�u �m�s�

Summer

0 6 12 18hour

0.5

1.0

1.5

2.0�u �m�s�

0 6 12 18hour

0.5

1.0

1.5

2.0�u �m�s�

Autumn

0 6 12 18hour

0.5

1.0

1.5

2.0�u �m�s�

0 6 12 18hour

0.5

1.0

1.5

2.0�u �m�s�

Winter

0 6 12 18hour

0.5

1.0

1.5

2.0�u �m�s�

0 6 12 18hour

0.5

1.0

1.5

2.0�u �m�s�

Figure 2.3: Diurnal variations of the mean wind speed difference, Δu, between 100 and 60 mfor the western and eastern wind sectors at Høvsøre and for each season. Average over 5 yearsof cup anemometer measurements (2005–2009)

�

�

�

�

�

�

�

�

�

�

� 03:00� 15:00

6 8 10 12 1420

40

60

80

100

120

wind speed �m�s�

heig

ht�m�

116.5m100m

80m60m

40m

00:00 06:00 12:00 18:00 00:00

6

8

10

12

time

win

dsp

eed�m�s�

Figure 2.4: Time series of the wind speed at 5 heights and example of night time and day timeprofiles from East at Høvsøre on the 25/03/2007


20 Wind profiles

�

�

�

�

�

�

�

�

�

�

� 03:00� 15:00

12 14 1620

40

60

80

100

120


heig

ht�m� 116.5m

100m80m

60m40m

00:00 06:00 12:00 18:00 00:001011121314151617

time

win

dsp

eed�m�s�

Figure 2.5: Time series of the wind speed at 5 heights and example of night time and day timeprofiles from West at Høvsøre on the 05/04/2007

2.3.1 Stability

As shown previously, the ABL stability has a significant impact on the speed shear.Figure 2.6 shows the distribution of the relative wind speed difference between 100 and60 m by season for each sector considered in section 2.2.2.

As shown in Figure 2.3, the mean wind speed gradient is larger in winter than insummer. The distribution in spring shows the transition between summer and winterwith both a peak at low gradients and some very large shear.

Moreover, in each case are also shown the distribution of stable, neutral and unstableconditions. The stability was quantified with the Obukhov length, L, giving a measureof the degree of dominance of buoyancy over mechanical effects:

L = − u3∗ T

κg〈w′θ′v〉(2.1)

where u∗ is the friction velocity, κ is the von Kármán constant, taken here to be 0.4, g thegravitational acceleration, T the mean air layer temperature and 〈w′θ′v〉 the kinematicvirtual heat flux. Three stability classes were defined as follows:

• unstable: −500 < L < 0;• neutral: L < −500 or 500 < L;• stable: 0 < L < 500.

Figure 2.6 illustrates that, for the eastern sector, high shear coincides with stable condi-tions and low shear with unstable conditions. This is consistent with the fact that, foreasterly winds, the shear is mainly governed by the ABL stability. On the contrary, forwesterly winds, the correlation between the wind shear and the ABL stability is muchweaker because the wind speed profiles for this sector are influenced by the local effectsdue to the proximity of the coast. As the western sector is the sector of interest for thepower curve measurement at Høvsøre, the ABL stability was not chosen as the criterionto categorise the shear.

2.3.2 The logarithmic wind profile

The logarithmic wind profile relates the surface wind stress (here represented by u∗) tothe wind shear in the surface layer over homogeneous terrain in neutral conditions as:

u(z) =u∗κ

ln(

z

z0

)(2.2)

where u(z) is the mean wind speed at the height z and z0 is the roughness length. z0is the height where the downward extrapolated logarithmic velocity profile reaches zerovelocity. In the formulation here, variation due to stability and any displacement heightis ignored. However, in presence of high surface heat fluxes, such an approach tends tounderestimate the high-level wind speeds under stable conditions and to overestimate


Wind profiles 21

West East

Spring

All

Neutral

Stable

Unstable

�0.2 0.0 0.2 0.4�u�u60�m

10

20

30

40

50

60

70nb data ��

�0.2 0.0 0.2 0.4�u�u60�m

10

20

30

40

50

60

70nb data ��

Summer

�0.2 0.0 0.2 0.4�u�u60�m

10

20

30

40

50

60

70nb data ��

�0.2 0.0 0.2 0.4�u�u60�m

10

20

30

40

50

60

70nb data ��

Autumn

�0.2 0.0 0.2 0.4�u�u60�m

10

20

30

40

50

60

70nb data ��

�0.2 0.0 0.2 0.4�u�u60�m

10

20

30

40

50

60

70nb data ��

Winter

�0.2 0.0 0.2 0.4�u�u60�m

10

20

30

40

50

60

70nb data ��

�0.2 0.0 0.2 0.4�u�u60�m

10

20

30

40

50

60

70nb data ��

Figure 2.6: Distribution of the wind speed difference between 100 and 60 m, Δu, normalisedwith the wind speed at 60 m, u60 m, for all data and each stability class, for the western andeastern sectors at Høvsøre and for each season. The results are given as percentage of the numberof data (nb data). Results obtained for 5 years of cup anemometer measurements (2005–2009).

them under unstable conditions. According to the Monin-Obukhov similarity theory(MOST), the wind speed gradient is a function of the stability parameter z/L (Moninand Obukhov, 1954). For unstable and stable conditions, the wind speed profile is givenby:

u(z) =u∗κ

[ln

(z

z0

)− ψm

( zL

)](2.3)

where ψm is the correction function of the logarithmic profile for stability and its formdepends on the sign of L. However MOST is applicable only in homogeneous surfacelayers which might differ at coastal sites, for example. This is illustrated in Figure2.7 which shows, for each sector separately, the dimensionless shear (φm) at 40 m as afunction of the stability parameter z/L at z = 20 m. The wind speed gradient, ∂u/∂z,


22 Wind profiles

was derived from cup anemometer measurements at 6 heights, 10–116.5 m, from theHøvsøre met. mast. These measurements were fitted to a second-order polynomial inln(z):

U = U0 + A ln(z) + B ln(z)2 (2.4)

where U0, A and B are fitted parameters determined by a least-squares method. Thedimensionless wind shear was then obtained by differentiation and normalisation ofeq. (2.4):

φm =κz

u∗∂u

∂z=

κ

u∗(A + 2B ln(z)) (2.5)

�4 �2 0 2 4�1

0

1

2

3

4

5

6

z�L

Φ m

West

�4 �2 0 2 4�1

0

1

2

3

4

5

6

z�L

Φ m

East

Figure 2.7: Dimensionless wind shear φm as function of the stability parameter z/L. The bluedots represent the measurements at Høvsøre. The gray solid line corresponds to a theoreticalsuggestion from (Högström, 1971).

Figure 2.7 shows that measurements from the eastern sector follow better MOSTthan those from the western sector. For the eastern sector, the upstream terrain ismainly characterised by flat farm land and the surface layer is rather homogeneous. Forthe western sector, the horizontal homogeneity criterion is violated by the presence ofan upstream coast. For this sector, the shear is lower than the prediction in unstableconditions, whereas it is higher in the neutral region. Under stable conditions, φm isbroadly distributed and seems to split in different branches, which are probably due toseasonal variations.

2.3.3 Vertical wind gradient

Another approach is to characterise each profile with its gradient at a given height.Based on the approach of section 2.3.2, the wind gradient, ∂u/∂z, at 40 m was derivedfrom differentiation of eq. (2.4). As it is based on a fit to a polynomial, the accuracyof this approach depends on the number of measurement points available. This issue isillustrated in Figure 2.8 (a) showing an example of a measured profile together with thedifferent curves obtained by fitting different measurement points. Figure 2.8 (b) showsthat the distributions of the wind gradient strongly depend on the number of points,demonstrating that this result is quite general.

Consistent comparison of the wind shear at different sites with this method requiresmeasurements at the same heights at all sites (same number and same altitudes).

2.3.4 The power law profile

For structural purposes, the power law profile has been used most widely because of itssimplicity:

u(z) = u(zref )(

z

zref

)α(2.6)

where u(zref ) is the wind speed at a reference height zref and α is the shear exponent.It was first introduced by Davenport (1960) to represent the wind speed profile in the


Wind profiles 23

� measurementsfit 6 pointsfit 10m, 40m, 60mfit 5 pointsfit 40m, 60m, 80m

�a�4 6 8 10

0

20

40

60

80

100

120

140


heig

ht�m�

� � � � � � � � �

�

�

�

�

�

� �

�

�

�

�

�

��

�

�

��

�

�

�

�

�

��

�

�

�

�

��

�

�

��

��

�

�

�

�

��

��

��

��

�

�

�

�

� ��

��

�

��

�

��

� fit 6 points

� fit 10m, 40m, 60m� fit 5 points

� fit 40m, 60m, 80m

�b��0.05 0.00 0.05 0.10 0.150

2

4

6

8

10

�u��z

num

ber

ofpr

ofile

s��

Figure 2.8: (a) Example of a wind profile measured by the met. mast at Høvsøre and the differentcurves obtained by fitting the measurements at 6 points (10–116.5 m), at the 3 lowest points (10,40, 60 m), at 5 points (40–116.5 m), at 3 points (40, 60, 80 m); (b) Distributions of the windgradient at 40 m obtained by differentiation of the different curves listed previously (Høvsøre,West sector, 2005–2009)

boundary layer as a function of the gradient wind speed. The power law has been broadlyaccepted in engineering applications and α is commonly estimated from measurementsat two heights on a met. mast:

α = log(

u(z2)u(z1)

)/ log

(z2z1

)(2.7)

where u(z1) and u(z2) are the wind speeds measured at the heights z1 and z2, respectively.The exponent increases with the roughness of the terrain, and decreases with increasinggeometric mean height (Tielmann, 2008). By suitable choice of α, the power law profileclosely corresponds to a considerable range of wind profiles compared to the other lessempirical forms, and it was found to provide a reasonable fit to the observed wind speedprofiles over a wide range of surface roughness and stability conditions (Perez et al., 2005).Based on measurements, Davenport (1960) suggested typical shear exponent values of1/7,1/3.5 and 1/2.5 for three roughness classes: grassland, forest and city, respectively.The IEC 61400-1 standard for wind turbine design specifies a normal wind shear withα = 0.2 (IEC, 1998b). However, numerous sites present shear exponent much larger than0.2 (Swalwell et al., 2008).

The derivation of the shear exponent from measurements at two heights can be crit-icized as it depends on the measurement heights. Figure 2.9 (a) shows an example of ameasured wind profile and the different power law profiles obtained by deriving the shearexponent from different pairs of measurement heights. Figure 2.9 (b) displays the distri-bution of the shear exponents obtained with different couples of measurement heights.The higher the measurement points, the smaller the shear exponent. This method fixesthe number of measurements points to 2, but a comparison of α for different sites is onlymeaningful when using identical measurement altitudes.

Furthermore the derivation of the whole wind profile from measurements at only twoheights can lead to an ambiguity as shown in Figure 2.10. This figure shows two differentmeasured profiles with very similar wind speed at 40 and 80 m, and the power law profilesderived from the wind speed measurements at those two heights. The power law profileis a poor representation of either of the two measured profiles and it is not possible todistinguish the two profiles from each other with this shear exponent.

A fit to three measurements may be more robust. However, if none of the mea-surement heights is above hub height, the shear exponent might not be representativeof the shear above hub height especially in case of influence of an IBL or for a LLJ.Moreover, the same problem as in section 2.3.3, related to the number and heights of themeasurements used to make the fit, is encountered.


24 Wind profiles

�

�

�

�

�

� measurementsΑ40�m,60�mΑ40�m,80�mΑ80�m,116�mΑ60�m,80�mΑ60�m,100�m

�a�6.0 6.5 7.0 7.5

0

20

40

60

80

100

120

140


heig

ht�m�

� �

�

�

�

�

�

� � � � ��

�

�

�

�

�

� � � � ��

�

�

�

�

��

�

�

�

�

�

�

� � � � ��

�

�

�

�

��

� Α40�m,60�m

� Α40�m,80�m

� Α80�m,116�m

� Α60�m,80�m

� Α60�m,100�m

�b��0.2 0.0 0.2 0.4 0.6 0.8

0

10

20

30

40

Α2�pts

num

ber

ofpr

ofile

s��

Figure 2.9: (a) Example of a wind profile measured with the met. mast at Høvsøre and the curvesfrom the power law for the different shear exponents considering measurements at 40-60 m, 40-80 m, 60-80 m, 80-116.5 m, 60-100 m; (b) Distributions of the shear exponents obtained witheq. (2.7) applied to the pairs of measurement heights listed previously (Høvsøre, West sector,2005–2009)

�

�

�

�

�

�

�

�

�

�� measuredprofile 1

� measuredprofile 2

power lawΑ0.197

6.0 6.5 7.0 7.5 8.0

40

60

80

100

120


heig

ht�m�

Figure 2.10: Example of two different observed wind profiles that are represented by the sameshear exponent if it is derived from eq. (2.7) at 40 and 80 m

Although the power law can represent a large range of wind speed profiles, it is limitedto wind shear increasing with altitude and wind speed. The only shear exponent cannotaccurately represent every 10 minute mean wind profile encountered during a power curvemeasurement.

2.3.5 Comparison of methods

The different methods used to characterise the wind shear, reviewed in this section, aresuitable to obtain the general tendency for the behavior of the wind speed profile at asite or for a wind sector, based on a long measurement periods (a year, for example).However, power performance measurements need to be performed in shorter time period.The IEC 61400-12-1 standard requires a minimum of 180 hours of measurements, whichcan typically be achieved in a few weeks.

The goodness of fit for various of the methods presented in this chapter was estimated.The goodness of fit was quantified by the residual sum of squares, RSS, derived from


Wind profiles 25

measurements at different heights:

RSS =N∑

i=1

(ufit(zi) − ui)2 (2.8)

where ufit is the fit function (polynomial or power law), ui is the wind speed measurementat the height zi, and N is the number of points where the residual is calculated (N = 5here).

The methods compared were:

• polynomial profile obtained by fitting of the speed measurements at 3 heights (40–80m) to eq. (2.4);

• power law profile obtained by fitting of the speed measurements at 3 heights (40–80m) to eq. (2.6);

• power law profile with a shear exponent calculated according to eq. (2.7) using thespeed measurements at 40 and 80 m;

• power law profile obtained by fitting of the speed measurements at 5 heights (40–116.5 m) to eq. (2.6).

The RSS distribution for the 4 methods are shown in Figure 2.11. Although all dis-tributions have their maximum at about RSS = 0.3, the best representation is obtainedwith the fit to the power law using 5 measurement points. Indeed, 90% of the RSSsobtained with this method are below 0.7, whereas, for the other methods using 2 or 3points, at least 21% of the RSSs are above 0.7. The best profile characterisation re-quires a reasonable number of measurement points that include observations above hubheight. Moreover, the RSS distributions for the power law profile derived from 2 and 3measurement heights are very similar. The polynomial approach is the poorest profilerepresentation, contrary to what one could expect given its extra degrees of freedom incomparison to the power law.

�

�

�

� ��

�

� �

�

��

�

�

�

�

��

� �

�

��

�

�

�

�

�

�

�

��

� � � � � � � � ��

�

�

� �

�

��

�

� � � � � � � � � � �

� polynomial fit 3pts� power law fit 3points� power law 2 points

� power law fit 5 points

0.0 0.5 1.0 1.5 2.00

5

10

15

20

RSS

num

ber

ofpr

ofile

s��

Figure 2.11: Distribution of RSS (eq. (2.8)) for 4 methods used to represent the wind profile


Chapter 3

Effect of speed shear on thepower performance

The previous chapter showed how variable the wind speed profile can be depending onmany parameters such as the geographical location, the wind direction, the season andthe time of the day. Seasonal effects on the power output of a turbine have been shown inflat terrain and it was demonstrated that they were due to the seasonal variations of thewind characteristics such as shear and turbulence. The relation between turbine poweroutput variations and shear variations was shown in previous investigations. A reviewof the main investigations is given as the first part of this chapter. Then, a preliminarystudy, based on aerodynamic simulations, shows how the shear is related to the poweroutput variations by simulating the response of the turbine in a sheared inflow. Thisshort study also shows the consequence of these variations on the power curve which isthe main theme of this thesis.

3.1 Literature review

The effect of the wind shear on the power performance of a wind turbine was the sub-ject of a few earlier investigations. The analysis of the influence of the wind shear onthe power performance of a wind turbine is not easy because of the lack of the neces-sary measurements. Indeed, when shear measurements are available (generally at testssites dedicated to research), power data are not available, whereas, when power dataare available (for instance where a power performance verification is performed), shearmeasurements are often lacking.

Sumner and Masson (2006) investigated the effect of atmospheric stability on windturbine power performance. Missing speed profile measurements, the authors used theirmodel, based on the Monin-Obukhov similarity theory, to derive the wind speed profilesfrom speed and temperature measurements at hub height. They found that the variationin wind speed over the rotor swept area had some effect on the power performance andthat characterising the energy with the wind speed at hub height generally overestimatethe resource. For the site considered, the difference in annual energy production (AEP)calculated using hub height and disk average wind speed was on the order of 5%. Theseresults were generated for a wind park located in very simple terrain. Larger differencescould be expected for higher roughness. However, it was shown in chapter 2 that nu-merous parameters other than the ABL stability could influence the speed profiles. Theprofile model used in (Sumner and Masson, 2006) would probably shows some limita-tions at coastal sites or in places experiencing low level jets. For example, Antoniou et al.(2009) found two different power curves by considering day time and night time mea-surements separately, in the US Midwest, resulting in an increase in AEP of 3% duringthe nigh time. No shear measurements were available at the turbine site, but previousstudies had shown that low level jets occurred frequently at night in that region. The


28 Effect of speed shear

authors used an aerodynamic model to simulate the power output of their turbine incase of such a LLJ. They found an increase in power comparable to that they measuredduring night. These two investigations showed that the power variations coincide withthe shear variations. However, assumptions on the speed profiles had to be made.

Other investigations included both speed profile and power measurements. VanLuva-nee et al. (2009), for example, categorised measured profiles in two groups: the profilespresenting a low level jet on the one hand, and the profile following a power law onthe other hand. Combined with power measurements, these two groups of data resultedin two different power curves. The low level jets gave more power than the power lawprofiles. Elliott and Cadogan (1990) obtained different power curves for different turbu-lence intensities, however the difference between the power curves was larger than whatcould be expected from differences in turbulence intensity. Further investigations showedthat the large differences were due to speed shear. During low turbulence conditions,they observed strong shear in the lower half of the rotor and weak or negative in theupper half. The authors concluded that a significant error in power curve measurementcould result if the effect of shear was ignored and that with increasing rotor diameter,the hub height wind speed generally became less representative of the disk average windspeed. This investigation also pointed out that it is important to distinguish the effectsof the different parameters such as turbulence and shear, which is not always easy todo with measurements as these parameters are often correlated. For example, a stablystratified surface layer generally implies low turbulence and high shear. At the otherextreme, under unstable conditions, the turbulence intensity is generally high and thespeed profile nearly constant because of the thermal mixing (see chapter 2). This wasalso shown by Albers et al. (2007) who investigated the power curve measurements ofthree multi-megawatt wind turbines in flat terrain. The wind shear was characterisedby a gradient derived from wind speed measurements at two heights (hub height andbelow). The data were binned according to the vertical speed gradient but also to theturbulence intensity in order to isolate the shear effect from the turbulence effects. Highshear resulted in lower power output than low shear for the turbine with the lowest hubheight (therefore experiencing the highest speed gradient), whereas no clear effect of theshear was observed for the two other turbines.

All these investigations showed that speed shear had an influence on the power outputof a wind turbine which leads to variations in the power curve. They also showed thatinvestigating the effects of wind shear and turbulence on the turbine power output is notstraightforward since these parameters are correlated. Because of this correlation, it isdifficult to investigate the influence on the power output of shear independently of turbu-lence. Numerical models of wind turbine aerodynamics make possible the investigation ofthe effect of various parameters independently of each other. Walter (2007) performed anadvanced analysis of the variations of shear in Texas. Lacking power measurements, heused a blade element momentum (BEM) model to simulate the power output of a largewind turbine subjected to various inflows characterised by different shear exponents. Hisresults showed a decrease in power compared to the power obtained with uniform inflow.

3.2 Aerodynamic simulations set up

The influence of a non-uniform flow on the mechanical power output of a horizontal axiswind turbine is complicated since each section of the rotor blade is subjected to spatiallyand temporally varying wind during rotation. The use of aerodynamic simulations isa good tool in order to get a better understanding of what difference a sheared inflowmakes for a turbine compared to an uniform inflow. It was therefore chosen to make apreliminary investigation with such a tool.

3.2.1 Aerodynamic model

The turbine modeled was a 3.6 MW Siemens, with a rotor diameter of 107 m, hub heightof 90 m and a variable-speed, variable-(collective) pitch control strategy. The aerody-


Effect of speed shear 29

namics of the turbine were simulated with HAWC2Aero (Larsen, 2008). This modelsimulates, in the time domain, the response of a rigid rotor subjected to aerodynamicforces. The code is a simplified version of the full aeroelastic code HAWC2 (Larsen,2007) with a different (rigid) structural model. The aerodynamic part of the code isbased on the BEM theory, but extended from the classic approach to handle dynamicinflow, dynamic stall, skew inflow and shear effects on the induction (Larsen and Hansen,2006). Apart from a simplified structural formulation, all other substructures of the codein HAWC2 and HAWC2Aero are identical. In HAWC2Aero the rotor is assumed rigidwhich leaves only one degree of freedom namely the rotor rotation, whereas the HAWC2code is based on a multibody formulation with very few limitations on the structurallayout. The controller would change the pitch angle though, but only for wind speedsabove rated power (which are not of interest in this study). The main benefit of theHAWC2Aero code is the simulation speed (approximately 10 times faster than real timeon a standard pc) and the reduced complexity of the input parameters compared to thefull HAWC2 code.

In order to check if the rigid structure simplification was acceptable, simulations withthe full HAWC2 model were run for a typical multi-MW wind turbine1, for both cases ofelastic and rigid structures. For each type of structure, various wind speed at hub heightwere considered, and, for each wind speed, two kinds of profiles: a uniform profile (samewind speed at all heights) and a power law profile with a shear exponent of 0.5. Thedifference in power output obtained for those two kinds of profiles is shown in Figure 3.1for an elastic structure on one hand and for a stiff structure on the other hand.

�

�

�

��

�

�

� �

�

�

�

��

�

�

� �

� Rigid� Elastic

6 8 10 12uhub

�0.04

�0.03

�0.02

�0.01

�Pshear�Pflat��Pflat

Figure 3.1: Wind shear effect on the power output for a rigid structure and an elastic structure.Relative power output obtained with simulations carried out with full HAWC2 model for a fictive5MW wind turbine with a uniform inflow and a sheared inflow (power law with shear exponentof 0.5).

Figure 3.1 shows that, for the elastic structure, the shear effect on the power output isslightly larger than with the stiff model. However, the difference between the two modelsis rather small (less than 1% on average). It was therefore assumed for the rest of theinvestigation that the results obtained with a rigid structural model were representativeof the effect of shear on the power performance. Moreover, the fictive wind turbine wasmodelled with parameter values typical for a modern multi-MW wind turbine. Theseresults are therefore expected to be comparable for the simulations of any multi-MWturbines, similar in concept.

3.2.2 Model limitations

The BEM model is based on a number of assumptions for the flow properties in order toderive simple relations for the axial and tangential induction. One of these assumptions isto ignore the pressure term from the rotation of the wake. Madsen et al. (2007) showed

1the 5MW reference wind turbine defined by Jonkman et al. (2009)



that it resulted in an overestimation of the induction in the inner part of the rotor.Moreover, the BEM model does not account for the wake expansion which results in anunderestimation of the induction at the tip region.

Furthermore, complicated aerodynamics occur when a horizontal axis wind turbineoperates in shear inflow. The existence of wind shear in the free stream can createsubstantial asymmetries and non periodicities in the structure of the wake behind therotor (Sezer-Uzol and Uzol, 2009). Zahle and Sørensen (2008) showed that the wind shearresulted in tilting the wake and that the wake expands asymmetrically. This causes a non-uniform induced flow over the rotor which varies with the azimuth position of the blade.However, the classical BEM model assumes a constant induction factor for a given radiusas the equations are solved for each annulus independently from the adjacent annuli.

For this reason, the BEM model used in HAWC2 was modified so that the inducedvelocity varies with azimuth angle. “The characteristic of this implementation of BEMwith respect to wind shear is that the local thrust coefficient is based on the local loadsof the blade at this specific point but normalized with the free stream velocity averagedover the whole rotor disc. The final induced velocity will thus vary along the blade as afunction of azimuth position of the blade” (Bak, 2006).

This code was compared to a classic BEM code, Flex5, and two more advanced mod-els, the Actuator Line model and the CFD based EllipSys3D code, in (Madsen, 2008)and (Madsen et al., 2010). In these investigations, the more advanced models showedthe variations of axial induction with azimuth position. A serious concern for the inves-tigation made in this chapter is the fact that some models showed that a sheared inflowresulted in a decrease of the power output whereas others show an increase (see Table3.1). There is therefore a high uncertainty regarding the influence of wind shear on theturbine rotor, probably because the induction was implemented in different ways in thevarious models. Even the more advanced models did not demonstrate any convergence,thus not allowing any conclusions as to the correct method.

El. Power El. Power[kW] [kW]

no shear shearHAWC2 1928 1870

EllipSys3D 1937 2036FLEX5 1958 1958AC-Line 1958 1942

Table 3.1: Comparison of electrical power at 8 m/s for uniform inflow and shear inflow (powerlaw with exponent of 0.5), from (Madsen et al., 2010).

The results from the investigation presented here are therefore restricted to HAWC2Aeroand the underlying modeling assumptions and uncertainties must be remembered. De-spite the high uncertainty of the results, HAWC2Aero was a good compromise as it isbased on an improved BEM model that is believed to model the underlying physics in aconvincing manner, and yet has a low computational time.

The turbine modeled was a 3.6 MW Siemens, with a rotor diameter of 107m, hubheight of 90 m and a variable-speed, variable-(collective) pitch control strategy. Therotation speed was limited to a maximum of 1.963 rad/s for noise reduction. Once thismaximum is reached for a given wind speed (about 5m/s), the rotation speed remainsconstant for higher wind speeds.

In order to restrict the variations in power to the variations due to the speed shear(and not to any other effect), each case is assumed as idealised as possible. The lowerpart of the boundary layer (corresponding to the “turbine layer” where the turbine rotorstands) is assumed horizontally homogeneous. The wind speed can vary vertically, butis uniform in horizontal planes at each height: u(x, y, z) = u(z) = (ux(z), uy(z), uz(z)) .This assumption is fair to model the surface layer over flat terrain. Moreover, the towershadow effect is turned off. The tower shadow induces a 3p oscillations of the loads on the



rotor with a larger amplitude than that due to shear (Dolan and Lehn, 2006) but it doesnot significantly influence the difference in power output between constant and shearedinflows. Finally, the shaft tilt angle was set to 0◦, in order to be able to observe theazimuth dependent variations of the angle of attack and the relative speed experiencedby the blade due to the wind shear. The tilt angle results in oscillations of the loads witha different phase and larger amplitude than that due to the shear alone. It may thereforereduce the effect of the wind shear on the power performance but it was neglected herein order to focus on the effect of the wind shear.

3.3 Effect of the wind speed shear on the aerodynam-ics of the turbine

This section aims at showing the differences a sheared inflow makes in the aerodynamicsof the turbine compared to a uniform inflow. In order to focus on the vertical variationof the horizontal wind speed on the power output of the turbine, the results presentedin this section were all obtained with laminar inflow (no turbulence).

3.3.1 Free wind speed

The simulations results obtained with a sheared inflow, defined by a power law (seeeq. (2.6)) with a shear exponent of 0.5, are compared to the results obtained with aconstant inflow. Both speed profiles have the same wind speed at hub height: 8 m/s;they are shown in Figure 3.2.

4 6 8 10wind speed �m�s�

40

60

80

100

120

140

height �m�

Figure 3.2: Profiles used as input. Black: constant profile (i.e. no shear); Blue: power lawprofile with a shear exponent of 0.5. Both profiles have the same wind speed at hub height.

Figure 3.3 shows the free wind speed (i.e. wind speed as if there were no turbine) seenby a point at a radius of 30m from the rotor centre and rotating at the same speed asthe rotor as a function of time. Whereas in a uniform inflow the point is subjected to aconstant wind speed, in a sheared flow, the point is exposed to large variations of windspeed (even though the inflow is laminar). The variation of the wind speed seen by thispoint in time is only due to the fact that it is rotating within a non uniform flow (speedvarying with altitude).

Figure 3.4 shows the variations of the free wind speed seen by the same rotating pointas previously but as a function of the azimuth position (0◦ corresponds to the downwardsposition). The point experiences the hub height wind speed at ±90◦, lower wind speedwhen it is downward (0◦) and higher wind speed when it is upward (180◦). As the windspeed increases with height in the case of the power law profile, the amplitude of thevariations of the free wind speed seen by a rotating point increases with the radius (notshown here), whereas for a uniform flow, the free wind speed is the same whatever theposition on the swept rotor disc (any radius, any azimuth).



120 140 160 180 200time�s�

7.07.58.08.59.0

uy �m�s�

Figure 3.3: Time series of free wind speed seen from a rotating point, positioned at a radius of30m, rotating at rotor speed. Black: no shear; Blue: power law profile with shear exponent of0.5.

�150 �100 �50 50 100 150Θ ��

7.0

7.5

8.0

8.5

9.0

uy �m�s�

Figure 3.4: Free wind speed seen from a rotating point, positioned at a radius of 30m, as afunction of the azimuth angle. Black: no shear; Blue: power law profile with shear exponent of0.5.(0◦ corresponds to downwards)

3.3.2 Relative speed and angle of attack

A rotating blade does not experience the free wind speed because of the induction dueto the drag of the rotor. The forces acting on the rotating blade are directly relatedto the relative speed - i.e. the speed of the wind passing over the airfoil relative to therotating blade - and the angle of attack - i.e. the angle between the blade chord line andthe relative wind speed - which depends on the induced speed, see Figure 3.5.

rotation

r�

uiw

�

Figure 3.5: Speed triangle for a blade element. ui is the induced wind speed, rΩ the opposite ofblade speed at this radius, w the relative speed and Φ the angle between the rotor plane and wcorresponding to the sum of the pitch angle, the twist angle and the angle of attack.

The variations of the relative speed and the angle of attack as a function of the bladeazimuth angle are shown in Figure 3.6. These two parameters vary with the azimuthangle in a sheared inflow whereas they remain constant in a uniform inflow.

The relative speed and the angle of attack are derived from the rotor speed and theinduced velocity, therefore they depend on the way the induction is modeled. It appearsthat it is difficult to evaluate their variations due to a non uniform flow in a simple way.However, some basic considerations, ignoring the induction, can give a basic insight tothe variation of the relative speed and the angle of attack as the blade rotates in a sheared



�a��150 �100 �50 50 100 150

Θ ��

2.5

3.0

3.5

4.0

angle of attack ��

�b��150 �100 �50 0 50 100 150

Θ ��

43.0

43.5

44.0

44.5

45.0Vrel �m�s�

Figure 3.6: (a): Angle of attack and (b): relative speed as a function of the azimuth angle, seenfrom a point at radius r=30m on a rotating blade. Black: no shear; Blue: power law profile withshear exponent of 0.5.

inflow. When the blade points upward, the free wind speed increases compared to thewind speed at hub height (or uniform inflow case), and so does the relative speed andthe angle of attack, see Figure 3.7 (right). Inversely, when the blade points downward,they decrease, see Figure 3.7 (left).

rotation

r�

uw

�

Blade downwards

rotation

r�

uw

�

Blade upwards

Figure 3.7: Simplified speed triangles for an upward and downward blade showing the effect ofwind speed shear. The speed triangle for a horizontal blade is shown with dashed arrows. As thetwist angle is constant for a given position on the blade and the pitch angle is 0◦ for wind speedbelow rated speed, the variations of Φ represents the variation of the angle of attack.

3.3.3 Tangential force and Torque

The angle of attack and relative speed variations result in a variation of the local lift anddrag as the blade rotates, which in turn results in the variation of the local tangentialforce, see Figure 3.8. The angle Φ, the local lift (dFL) and the local drag(dFD) wereobtained as output of the model and the local tangential force (dFT ) is given by:

dFT = dFLCos(Φ) − dFDSin(Φ) (3.1)

The torque depends on the integral of the tangential force over the whole rotor, henceit does not only depend on the wind speed at hub height but also on the distribution ofthe speed over the rotor. As shown in Figure 3.9, the torque obtained with a shearedinflow has a small 3p oscillation and the mean torque is lower that the torque obtainedfor uniform inflow.

3.4 Consequences on the power production

In order to look at the effect of speed shear on the power output of the turbine, simulationswere run for various shear exponents between -0.1 and +0.5 and for a range of wind speedsat hub height from 5 to 10 m/s.



�a�

�150 �100 �50 0 50 100 150Θ ��

2.0

2.2

2.4

2.6

2.8

dFL �kN�m�

�b�

�150 �100 �50 0 50 100 150Θ ��

0.030

0.032

0.034

0.036

0.038dFD �kN�m�

�c��150 �100 �50 0 50 100 150

Θ ��

0.05

0.10

0.15

0.20

dFT �kN�m�

Figure 3.8: (a): Local lift , (b): local drag , (c): local tangential force seen from a point atradius r=30m on a rotating blade as a function of its azimuth position. Black: no shear; Blue:power law profile with shear exponent of 0.5.

�150 �100 �50 50 100 150Θ ��

930

940

950

Q �kNm�

Figure 3.9: Total torque as a function of the azimuth position. Black: no shear; Blue: powerlaw profile with shear exponent of 0.5.

Figure 3.10 shows the relative difference between the power output obtained for asheared profile (P (α)uhub) and the power output obtained with a uniform inflow for thesame wind speed at hub height, (P (0)uhub):

ΔP =P

(α)uhub − P (0)uhub

P(0)uhub

(3.2)

According to HAWC2Aero, the power output depends on the shear exponent, mainlyresulting in a decrease of the power when the shear exponent increases. These results areconsistent with Walter (2007) and Antoniou et al. (2009) who carried out the same kindof simulations with BEM models and power law profiles. Moreover, it coincides with themeasurements presented in (Albers et al., 2007), where high shears gave smaller poweroutputs than low shear. This shows that power law profiles are expected to give lowerpower than constant profiles. However it does not mean that large shear necessarilyresults in lower power. Antoniou et al. (2009) and VanLuvanee et al. (2009) showed thatprofiles influenced by low level jets, characterised with higher shear above hub heightthan below hub height, resulted in higher power than other profiles (constant or powerlaw).



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� �P for uhub5 m�s� �P for uhub6 m�s� �P for uhub7 m�s� �P for uhub8 m�s� �P for uhub9 m�sO �P for uhub10 m�s� �KE

�0.2 �0.1 0.1 0.2 0.3 0.4 0.5Α

�10

�5

5

10

��

Figure 3.10: Normalised difference in power output and in kinetic energy flux between shearedinflow and uniform inflow as function of the shear exponent, for various wind speeds at hubheight. (The difference in kinetic energy flux is explained in section 5.2.1.)

3.5 Consequences on the power curve

3.5.1 With power law profiles

As explained in chapter 1, a power curve shows the power output of the turbine as afunction of the wind speed at hub height. However, as shown previously, for a givenwind speed at hub height, the power output of a turbine is expected to vary with thewind speed shear. This variation in the power output results in a significant scatter inthe power curve plot as the shear varies during the power curve measurement. Indeed, ifonly the wind speed at hub height is considered, all the points corresponding to profileswith the same wind speed at hub height appear with the same abscissa but with differentordinates, since the different profiles result in different power out

accounting for the speed shear in wind turbine power … · author: rozenn wagner title: accounting...

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